Answer
$-15i+9j-18k$
Work Step by Step
Given that, $\vec A=15i-40j,\space \vec B=31j+18k$
Let's take, $\vec C=xi+yj+zk$
We can write,
$\vec A+\vec B+\vec C =(15i-40j)+(31j+18k)+(xi+yj+zk)$
$\vec A+\vec B+\vec C= (15+x)i+(y+31-40)j+(18+z)k$
If, $\vec A+\vec B+\vec C=0$, we can write
$15+x=0$
$x=-15$
$y+31-40=0$
$y=9$
$18+z=0$
$z=-18$
Then we can write, $\vec C=15i+9j-18k$
